Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I

Average Error: 3.3 → 0.4

Time: 5.2s

Precision: binary64

\[[y, z] = \mathsf{sort}([y, z]) \\]

Math

\[x \cdot \left(1 - y \cdot z\right) \]

↓

\[\begin{array}{l} t_0 := -y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;y \cdot z \leq -1.257058379857181 \cdot 10^{+243}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \cdot z \leq 2.952490036847228 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* y (* z x)))))
   (if (<= (* y z) -1.257058379857181e+243)
     t_0
     (if (<= (* y z) 2.952490036847228e+151) (* x (- 1.0 (* y z))) t_0))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

↓

double code(double x, double y, double z) {
	double t_0 = -(y * (z * x));
	double tmp;
	if ((y * z) <= -1.257058379857181e+243) {
		tmp = t_0;
	} else if ((y * z) <= 2.952490036847228e+151) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - (y * z))
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -(y * (z * x))
    if ((y * z) <= (-1.257058379857181d+243)) then
        tmp = t_0
    else if ((y * z) <= 2.952490036847228d+151) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

↓

public static double code(double x, double y, double z) {
	double t_0 = -(y * (z * x));
	double tmp;
	if ((y * z) <= -1.257058379857181e+243) {
		tmp = t_0;
	} else if ((y * z) <= 2.952490036847228e+151) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

↓

def code(x, y, z):
	t_0 = -(y * (z * x))
	tmp = 0
	if (y * z) <= -1.257058379857181e+243:
		tmp = t_0
	elif (y * z) <= 2.952490036847228e+151:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

↓

function code(x, y, z)
	t_0 = Float64(-Float64(y * Float64(z * x)))
	tmp = 0.0
	if (Float64(y * z) <= -1.257058379857181e+243)
		tmp = t_0;
	elseif (Float64(y * z) <= 2.952490036847228e+151)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

↓

function tmp_2 = code(x, y, z)
	t_0 = -(y * (z * x));
	tmp = 0.0;
	if ((y * z) <= -1.257058379857181e+243)
		tmp = t_0;
	elseif ((y * z) <= 2.952490036847228e+151)
		tmp = x * (1.0 - (y * z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := Block[{t$95$0 = (-N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(y * z), $MachinePrecision], -1.257058379857181e+243], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2.952490036847228e+151], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.2570583798571811e243 or 2.9524900368472281e151 < (*.f64 y z)

   1. Initial program 23.0

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Applied egg-rr 23.6

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - y \cdot z\right)}\right)}^{3}} \]

   3. Applied egg-rr 23.6

      \[\leadsto \color{blue}{{\left(\sqrt[3]{1 - y \cdot z}\right)}^{2} \cdot \left(\sqrt[3]{1 - y \cdot z} \cdot x\right)} \]

   4. Applied egg-rr 23.8

      \[\leadsto {\left(\sqrt[3]{1 - y \cdot z}\right)}^{2} \cdot \left(\color{blue}{{\left(\sqrt[3]{\sqrt[3]{1 - y \cdot z}}\right)}^{3}} \cdot x\right) \]

   5. Taylor expanded in y around inf 2.2

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]

   6. Simplified 2.2

      \[\leadsto \color{blue}{-y \cdot \left(x \cdot z\right)} \]

   if -1.2570583798571811e243 < (*.f64 y z) < 2.9524900368472281e151

   1. Initial program 0.1

      \[x \cdot \left(1 - y \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.257058379857181 \cdot 10^{+243}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 2.952490036847228 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022133 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))